Simplify the following expression: $ q = \dfrac{4}{5} - \dfrac{-1}{n + 5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{n + 5}{n + 5}$ $ \dfrac{4}{5} \times \dfrac{n + 5}{n + 5} = \dfrac{4n + 20}{5n + 25} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-1}{n + 5} \times \dfrac{5}{5} = \dfrac{-5}{5n + 25} $ Therefore $ q = \dfrac{4n + 20}{5n + 25} - \dfrac{-5}{5n + 25} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{4n + 20 + 5 }{5n + 25} $ Distribute the negative sign: $q = \dfrac{4n + 20 + 5}{5n + 25}$ $q = \dfrac{4n + 25}{5n + 25}$